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An Introduction to Incidence Geometry

  • Bart De Bruyn

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Bart De Bruyn
    Pages 1-10
  3. Bart De Bruyn
    Pages 11-37
  4. Bart De Bruyn
    Pages 61-88
  5. Bart De Bruyn
    Pages 89-127
  6. Bart De Bruyn
    Pages 129-164
  7. Bart De Bruyn
    Pages 165-250
  8. Bart De Bruyn
    Pages 251-273
  9. Bart De Bruyn
    Pages 275-302
  10. Back Matter
    Pages 303-372

About this book

Introduction

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs.

 This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.

Keywords

projective spaces incidence geometry polar spaces strongly regular graphs distance-regular graphs generalized polygons near polygons dual polar spaces designs

Authors and affiliations

  • Bart De Bruyn
    • 1
  1. 1.Department of MathematicsGhent UniversityGhentBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-43811-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-43810-8
  • Online ISBN 978-3-319-43811-5
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site